stature and body mass estimation from skeletal remains in the … · 2014-02-28 · stature and...

Stature and Body Mass Estimation From SkeletalRemains in the European Holocene

Christopher B. Ruff,1* Brigitte M. Holt,2 Markku Niskanen,3 Vladimir Sladek,4 Margit Berner,5

Evan Garofalo,1 Heather M. Garvin,1 Martin Hora,4 Heli Maijanen,3 Sirpa Niinimaki,3 Kati Salo,6

Eliska Schuplerova,4 and Dannielle Tompkins2

1Center for Functional Anatomy and Evolution, Johns Hopkins University School of Medicine, Baltimore, MD 212052Department of Anthropology, University of Massachusetts, Amherst, MA 010033Department of Archeology, University of Oulu, Oulu 90014, Finland4Department of Anthropology and Human Genetics, Charles University in Prague, Prague 128 43, Czech Republic5Department of Anthropology, Natural History Museum, Vienna 1010, Austria6Department of Anthropology, University of Helsinki, Helsinki 00014, Finland

KEY WORDS body size; anatomical stature technique; long bones; femoral head

ABSTRACT Techniques that are currently availablefor estimating stature and body mass from Europeanskeletal remains are all subject to various limitations.Here, we develop new prediction equations based onlarge skeletal samples representing much of the conti-nent and temporal periods ranging from the Mesolithicto the 20th century. Anatomical reconstruction of stat-ure is carried out for 501 individuals, and body massis calculated from estimated stature and biiliac breadthin 1,145 individuals. These data are used to derivestature estimation formulae based on long bone

lengths and body mass estimation formulae based onfemoral head breadth. Prediction accuracy is superiorto that of previously available methods. No systematicgeographic or temporal variation in prediction errors isapparent, except in tibial estimation of stature, wherenorthern and southern European formulae are neces-sary because of the presence of relatively longer tibiaein southern samples. Thus, these equations shouldbe broadly applicable to European Holocene skeletalsamples. Am J Phys Anthropol 000:000–000, 2012.VVC 2012 Wiley Periodicals, Inc.

Body size estimation is an important component ofmany archeological and paleontological studies. Statureand body mass estimates have been used as indices ofpast health (Steckel and Rose, 2002; Cohen and Crane-Kramer, 2007) and sexual dimorphism (Smith and Horo-witz, 1984; Ruff, 2002), to study the effects of environ-mental variables such as subsistence strategy and cli-mate (Frayer, 1984; Ruff, 1994) as well as social status(Bogin and Keep, 1999) and as size ‘‘denominators’’ formany different parameters, including limb bonestrength, brain size, and body segment lengths orbreadths (Ruff et al., 1997; Weinstein, 2005; Rosenberget al., 2006; Ruff et al., 2006). For these reasons, it is im-portant that methods of estimating stature and bodymass in past populations should be as accurate as possi-ble. Several decisions are involved in this process: whichskeletal dimensions to use, which statistical approach toapply, and which reference sample(s) to use (Sjøvold,1990; Holliday and Ruff, 1997; Konigsberg et al., 1998;Auerbach and Ruff, 2004; Raxter et al., 2006; Kurki etal., 2010).Historically, stature estimation has received more

attention than body mass estimation, with a variety oftechniques now available (see Krogman and Iscan, 1986;Raxter et al., 2006; Vercellotti et al., 2009; Auerbach andRuff, 2010, and references therein). Stature estimationmethods can be divided into two basic categories: ‘‘math-ematical,’’ in which regression formulae (or ratios) basedon lengths of skeletal elements—usually long bones—areused to calculate stature, and ‘‘anatomical,’’ in whichindividual skeletal elements are summed to provide adirect stature estimate (Raxter et al., 2006). The mathe-

matical approach has the advantage that only singleskeletal elements are needed, but the disadvantage ofbeing dependent on the availability of an appropriaterecent reference sample of known or closely estimablestature (either cadaveric or living) and skeletal elementlengths. ‘‘Appropriate’’ has often been inferred to meanclosely related to the target sample in some way, forexample, geographically, temporally, genetically, and/orculturally. However, when dealing with skeletal samplesof populations from earlier time periods, it is often notpossible to closely match reference and target samples inthis way. Alternatively, an attempt can be made tomatch body proportions, such as intralimb segment

Additional Supporting Information may be found in the onlineversion of this article.

Grant sponsor: National Science Foundation; Grant numbers:0642297, 0642710. Grant sponsor: Grant Agency of the CzechRepublic; Grant numbers: 206/09/0589. Grant sponsor: Academy ofFinland and Finnish Cultural Foundation.

*Correspondence to: Dr. Christopher Ruff, Center for FunctionalAnatomy and Evolution, Johns Hopkins University School of Medi-cine, 1830 E. Monument St., Baltimore, MD 21205, USA.E-mail: [email protected]

Received 20 February 2012; accepted 2 April 2012

DOI 10.1002/ajpa.22087Published online in Wiley Online Library

(wileyonlinelibrary.com).

VVC 2012 WILEY PERIODICALS, INC.

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 000:000–000 (2012)

lengths, between reference and target samples (Hollidayand Ruff, 1997; Auerbach and Ruff, 2004), but this pro-vides only general guidance. For example, the correla-tion between crural index (tibia/femur length) and lowerlimb length/vertebral column height in a large modernskeletal sample was only 0.429 (Ruff et al., 2002).The ‘‘anatomical’’ approach to stature estimation, pio-

neered by Fully (1956) and recently modified by Raxteret al. (2006), has the advantage that body proportionsare not assumed or estimated but are intrinsicallyincluded in the measurements. The major disadvantageof the method is that it requires a largely complete skel-eton, a relatively rare occurrence in most archeologicalcontexts. Thus, exclusive use of this technique wouldgreatly reduce the number of specimens available forstudy. An alternative ‘‘hybrid’’ approach that is becomingmore commonly used in recent research is to estimatestature using the anatomical technique in a subset of asample or closely related samples, and use these staturesto calculate new regression formulae based on long bonelengths, which can then be applied to other less well-pre-served individuals (Feldesman and Lundy, 1988; Sciulliet al., 1990; Formicola and Franceschi, 1996; Sciulli andHetland, 2007; Raxter et al., 2008; Vercellotti et al.,2009; Auerbach and Ruff, 2010; Maijanen and Niskanen,2010).A number of different formulae have been used to esti-

mate stature from long bone lengths in European arche-ological material (e.g., see Sjøvold, 1990; Hanson, 1992;Formicola, 1993; Giannecchini and Moggi-Cecchi, 2008;Vercellotti et al., 2009; Meiklejohn and Babb, 2011).Among the most widely used formulae are those of Trot-ter and Gleser (1952, 1958), based on modern US sam-ples. However, problems with application of these andother available equations to earlier European skeletalsamples have been noted by various authors (Wells,1963; Hanson, 1992; Formicola, 1993; Maijanen and Nis-kanen, 2006; Vercellotti et al., 2009). These problemsmay be, at least in part, a function of variation in limblength to stature proportions between modern referenceand earlier European samples, although other statisticalissues may also be involved (Formicola, 1993, and seebelow). One way to evaluate the appropriateness of dif-ferent reference samples is to calculate the so-called‘‘Delta of Gini’’ parameter, which is the average differ-ence between stature estimates using different longbones from the same reference sample (Giannecchiniand Moggi-Cecchi, 2008; Shin et al., 2012). However, if apopulation is characterized by consistently shorter orlonger limbs relative to stature, compared with the refer-ence sample, consistency between stature estimatesderived from different long bones can still be associatedwith systematic directional bias in estimates. Only adirect measurement of stature, or the anatomical skele-tal equivalent, can reveal true proportional differences.This was the rationale for the development of several

sets of stature estimation equations for European arche-ological samples using the ‘‘hybrid’’ approach describedabove, whereby stature is first calculated with the ana-tomical method. Such equations have been developed fora sample of European Neolithic specimens (Formicolaand Franceschi, 1996), a Polish Medieval sample (Vercel-lotti et al., 2009), and a Swedish Medieval sample (Mai-janen and Niskanen, 2010) (in each study, total n 5 60).Although each of these studies provides valuable infor-mation, they are limited to either a specific region and/or temporal period. One purpose of the present study is

to extend the same type of analysis to a much largersample of specimens spanning the entire Holocene andmost of the European continent to generate morebroadly applicable equations.Body mass estimation from skeletal remains has been

less studied than stature estimation, but a number ofmethods have been recently proposed. As with statureestimation, body mass estimation can be divided intotwo basic approaches (Ruff, 2002; Auerbach and Ruff,2004). ‘‘Mechanical’’ approaches rely on the theoreticaland empirical relationship between body mass anddimensions of skeletal elements that mechanically sup-port body mass. Femoral head breadth has been mostcommonly used for this purpose (Grine et al., 1995; Ruffet al., 1997, 2006; Stock and Pfeiffer, 2001; Sladek et al.,2006; Kurki et al., 2010; Ruff, 2010), for a variety of rea-sons (Auerbach and Ruff, 2004). Three different regres-sion equations (or sets of equations) using femoral headbreadth are available, based on known or otherwise esti-mated body masses in recent human samples (Ruff etal., 1991; McHenry, 1992; Grine et al., 1995; see Auer-bach and Ruff, 2004; Ruff, 2010 for more discussion).None of these is specific to European populations,although all include some Euro-American data points intheir calculation (Ruff et al., 1991; McHenry, 1992 andJungers, personal communication).‘‘Morphometric’’ approaches to body mass estimation

attempt to reconstruct body size and shape directly frompreserved skeletal elements. Estimated stature combinedwith measured biiliac (maximum pelvic) breadth hasbeen shown to provide accurate estimates of body massin a wide variety of modern human populations (Ruff,1994, 2000), with some caveats (Ruff et al., 2005). Thistechnique has been applied to a number of archeologicaland paleontological specimens (Ruff, 1994; Arsuaga etal., 1999; Rosenberg et al., 2006; Ruff et al., 2006; Kurkiet al., 2010). The main advantage of the stature/biiliacmethod is that it does not rely on an assumed constantmechanical relationship between body mass and articu-lar size. For example, apparent allometric effects on therelationship between femoral head size and body masshave been documented, leading to recommendations touse different formulae in different size ranges (Auerbachand Ruff, 2004; Kurki et al., 2010; Ruff, 2010). In addi-tion, the available femoral head equations were derivedfrom only a limited number of modern human populationsamples, whereas the stature/biiliac method is based ona large number of populations that are likely to encom-pass the body size and shape of most recent humans(Ruff, 1994, 2000; Ruff et al., 2005). The disadvantage ofthe stature/biiliac approach is that it requires more skel-etal elements, in particular, a complete (or reconstruct-able) pelvis. Thus, morphometric body mass estimationis analogous to anatomical stature reconstruction, inmaking fewer assumptions but also being applicable tofewer specimens. Again, a ‘‘hybrid’’ approach is possible,by estimating body mass morphometrically in availablespecimens and using this as a baseline against which todevelop femoral head body mass estimation equationsfor less complete specimens. This is the approach takenin the current study.The final issue regarding both stature and body mass

estimation is which regression model to apply. This is acomplex question whose answer depends in part on howrepresentative the reference sample is of the target sam-ple (Konigsberg et al., 1998). In the present case,because of the very large size and geographic and tempo-

2 C.B. RUFF ET AL.

American Journal of Physical Anthropology

ral spread of the reference sample (see below), it is likelythat it encompasses the ranges of variation that wouldbe found in European archeological samples. However,even when target individuals fall within the size rangeof the reference sample, least squares (LSs) regression ofbody size on skeletal dimensions (‘‘inverse calibration’’ inthe terminology of Konigsberg et al., 1998), the mostcommonly used estimation technique, tends to producebiased results near the extremes of the size distribution,underestimating large individuals and overestimatingsmall individuals (Sjøvold, 1990; Maijanen and Niska-nen, 2010; also see Duyar and Pelin, 2003). Thus, ModelII regression techniques, in particular reduced majoraxis (RMA), have been suggested to provide more accu-rate estimates over a more extended size range (Sjøvold,1990; Aiello, 1992; Konigsberg et al., 1998; Maijanen andNiskanen, 2010). For this reason, the RMA technique ispreferred here.The aim of this study is to provide new stature and

body mass estimation equations that are broadly applica-ble to European Holocene adult skeletal samples. Stat-ure estimation equations are based on long bone lengths,with statures derived from anatomical reconstructions of501 individuals. Body mass estimation equations arebased on femoral head breadth, with body massesderived from stature and biiliac breadth determined in1,145 individuals. Comparisons are made to several pre-viously available methods. The potential effects of bothgeography and temporal period on estimation errors arealso evaluated.

MATERIALS AND METHODS

Skeletal samples

The samples used here are drawn from a larger on-going study of more than 2,000 individual skeletons(Ruff et al., 2012). Skeletal specimens were obtainedfrom museum collections across Europe, from time peri-ods ranging from Mesolithic to the 20th century. Com-plete listings of sites and numbers of individuals, bysex, are given in Supporting Information Tables S1 and

S2 for the samples used to develop stature and bodymass estimation equations, respectively. To assess possi-ble temporal and geographic variation in body propor-tions and thus applicability of different estimation equa-tions, the total samples were subdivided into sevenbroad geographic regions and eight general time peri-ods, summarized in Table 1. Regions include: 1) theBritish Isles (all from England), 2) Scandinavia (Swe-den, Denmark, and including Finland), 3) north-centralEurope (Germany, Czech Republic, and Austria), 4)France, 5) Italy, 6) the Iberian Peninsula (Spain andPortugal), and 7) the Balkans (Bosnia-Herzegovina andRomania). Time periods include: 1) very recent (�1900AD), 2) early recent (1600–1899 AD), 3) late Medieval(1000–1599 AD), 4) early Medieval (500–999 AD), 5)Iron Age/Roman (800 BC–499 AD), 6) Bronze Age(2300–1000 BC), 7) Neolithic (5000–2000 BC), and 8)Mesolithic (7000–4700 BC) (all dates calibrated). Thethree oldest periods overlap temporally because of re-gional variation in the timing of the Neolithic andBronze Age transitions (Milisauskas, 2002). Late Neo-lithic (Eneolithic) samples are included within the Neo-lithic. It should be noted that all of the samples fromFrance derive from the southern half of the country, i.e.,from below 468 N. latitude (see Supporting InformationTables S1 and S2).Males and females are relatively equally represented

in the samples, with a slight overrepresentation of males(268 males/233 females for stature and 624 males/521females for body mass). The same is true for each timeperiod and geographic region, with males constitutingbetween 42 and 68% of the temporal and regional sub-samples, except for the small Mesolithic and Bronze Agestature samples (Table 1), where males predominate(73–80%) (also see Supporting Information Tables S1and S2).All specimens included in the study were skeletally

adult, defined as having undergone fusion of all longbone epiphyses (almost complete fusion of the humeralhead was permissible). Ages were known for some of themost recent samples (Spitalfields, Luis Lopes, Siracu-sani, and Helsinki—see Supporting Information Tables

TABLE 1. Sample sizes by temporal period and regiona

Period Britain Scand. N-C France Italy Iberia Balkans Total

A. Stature estimationVery recent 0 0 0 0 9 50 0 59Early modern 24 20 0 10 21 0 0 75Late Medieval 14 73 14 0 2 15 39 157Early Medieval 0 0 39 2 8 6 0 55Iron/Roman 48 22 5 0 5 0 0 80Bronze 6 0 2 0 9 5 0 22Neolithic 3 16 12 16 1 0 0 48Mesolithic 0 2 0 0 0 0 3 5Total 95 133 72 28 55 76 42 501

B. Body mass estimationVery recent 0 40 0 0 9 49 0 98Early modern 40 21 0 16 13 0 0 90Late Medieval 103 153 61 0 5 30 49 401Early Medieval 0 0 99 7 13 37 0 156Iron/Roman 78 41 15 6 1 0 0 141Bronze 12 0 54 0 18 9 0 93Neolithic 11 66 51 18 4 0 0 150Mesolithic 0 7 0 0 0 1 8 16

Total 244 328 280 47 63 126 57 1,145

a See text and Supporting Information Tables 1 and 2 for details on temporal and regional classifications.

3EUROPEAN STATURE AND BODY MASS ESTIMATION


S1 and S2), and in the other samples, ages were esti-mated from skeletal indicators, primarily pubic symphy-seal morphology and relative dental wear (Miles, 1963;Brooks and Suchey, 1990), supplemented with cranialsuture closure, auricular surface morphology, and in theyoungest adults, late fusing pelvic, vertebral, and clavic-ular epiphyses and pseudoepiphyses (Buikstra and Ube-laker, 1994; Buckberry and Chamberlain, 2002; Falys etal., 2006). Precision of age estimates varied (from a fewyears to a decade or more) depending upon the agerange and the availability of age estimators. However, ithas been shown (Raxter et al., 2007) that use of evenbroad age categories is preferable to not consideringage at all when anatomically reconstructing stature(see below). In a few individuals, age could not bedetermined, in which case the average age of the entiresample (38 years) was assigned.Sex was determined primarily on the basis of pelvic

form, i.e., greater sciatic notch and subpubic morphology,supplemented with cranial features (Buikstra and Ube-laker, 1994; Bruzek, 2002). Individuals with gross path-ologies significantly affecting skeletal proportions, e.g.,rickets, were not included in the samples; however, otherless severe pathologies, including arthritis, did notconstitute criteria for exclusion.For use in stature estimation, maximum lengths of the

femur (Martin Fe1), tibia (including the malleolus andproximal spines, Martin Ti1a), humerus (Martin He1),and radius (Martin Ra1) were measured to the nearestmillimeter using an osteometric board. For use in bodymass estimation, superoinferior breadth of the femoralhead (Martin Fe18) was measured to the nearest 0.1 mmusing digital calipers. Other osteometric dimensionsincluded in stature and body mass analyses aredescribed further below.For the femur and tibia, either the right or left side

was chosen for measurement, choosing the best pre-served side or either side if the sides were equally wellpreserved. Directional bilateral asymmetry in lower limblengths and femoral head breadth is very small (\0.3%on average—see Auerbach and Ruff, 2006), so choice ofside has little effect. Bilateral asymmetry in upper limbbones lengths is somewhat larger (about 1% on aver-age—see Auerbach and Ruff, 2006). Both right and lefthumeri and radii, when present, were measured andincluded in stature analyses. Of the 501 individuals inthese analyses, 430 had both humeri, 37 only a rightand 26 only a left humerus, and eight individuals weremissing both sides. Three hundred ninety-three individu-als had both radii, 40 only a right and 40 only a left, and28 neither side. Right and left side values were averagedwhen both were present; otherwise, the single preservedside value was used. Because of the nearly equal repre-sentation of upper limb sides in the sample, this shouldnot have biased results. Given that the mean of rightand left side lengths is, on average, within about 0.5% ofeither side (see above), the slight loss in accuracy whenapplying the side-averaged equations to a single sidewas thought to be more than compensated by anincrease in simplicity of application.

Stature estimation

The Fully anatomical stature technique involves add-ing together the lengths or heights of the articulated ta-lus/calcaneus, tibia, femur, S1 through C2 vertebralbodies, and cranium (basion-bregma height) (Fully,

1956). A modification of this technique, including moreprecise definitions of skeletal dimensions and new for-mulae for converting skeletal to living stature, was usedhere (Raxter et al., 2006). Specifically, talus/calcaneusheight was measured with the articulated bones in ana-tomical position, and vertebral body heights were maxi-mum dimensions anterior to the pedicles. As recom-mended (Raxter et al., 2007), an age term was includedin the conversion to living stature (i.e., formula #1 inRaxter et al., 2006 was used). This modified techniquehas been found to provide excellent approximations toliving stature in subsequent comparisons (average resid-ual error\ 0.1%) (Maijanen, 2009).To increase sample sizes for anatomical reconstruc-

tions of stature, judicious estimation of a limited numberof missing elements is appropriate (see Auerbach, 2011,and references therein). Only about half (n 5 247) of theindividuals in our stature estimation sample preservedall 28 dimensions required by the anatomical staturereconstruction technique, with the others requiring esti-mation of at least one dimension. Here, we followed therecent recommendations provided by Auerbach (2011):basion-bregma height is not estimated from postcranialdimensions, femoral and tibial lengths are not estimated(from each other or from other dimensions), and verte-bral column length is not estimated from nonvertebralelements. In all of these cases, populations differ in pro-portions; thus, it is not possible to carry out estimationswithout assuming proportions a priori, which defeats thepurpose of the anatomical stature method. Therefore, allof the individuals in our sample had measurable femoraland tibial lengths, sufficient vertebrae to estimate verte-bral column height (see below), and basion-bregmaheight.Talocrural (TC) height can be estimated with reasona-

ble accuracy from tibial (T) and femoral (F) lengths,using sex-specific formulae (Auerbach, 2011). Wedeveloped our own formulae here (all dimensions inmillimeter):

ð1Þ Males ðn ¼ 656Þ : TC ¼ 0:094Fþ 0:036Tþ 15:9;

%SEE ¼ 7:6%

ð2Þ Females ðn ¼ 505Þ : TC ¼ 0:096Fþ 0:012Tþ 20:6;

%SEE ¼ 7:8%:

(Note that sample sizes are larger here because we tookadvantage of all available specimens in our overall sam-ple of [2,000 individuals. %SEE 5 percent standarderror of estimate.) Femoral and tibial lengths here referto those lengths used in the anatomical reconstructiontechnique (Raxter et al., 2006), i.e., femoral bicondylarlength (Martin Fe2) and tibial length measured from themalleolar tip to the lateral condyle (Martin Ti1). The rel-ative errors here are slightly greater than those of theequations reported (for a large sample of Native Ameri-can skeletons) by Auerbach (2011). Talocrural heightwas estimated in this way for 89 individuals (18%) ofour sample.The majority of the missing elements were, as usual

(Auerbach, 2011), individual vertebral body heights. Ofthe 501 individuals in our sample, 110 were missing sin-gle nonadjacent vertebrae, 51 were missing multiple ad-jacent vertebrae in the cervical region, and 93 weremissing multiple adjacent vertebrae in the thoracicregion. Single nonadjacent vertebral heights were esti-

4 C.B. RUFF ET AL.


mated by either averaging the heights of adjacent verte-brae or by using the formulae presented in Auerbach(2011), as appropriate (see Auerbach, 2011 for details).When multiple adjacent cervical vertebrae were missing,the combined heights of the lumbar and thoracic verte-brae were used to estimate total vertebral columnheight, and when multiple adjacent thoracic vertebraewere missing, the height of the combined lumbar verte-brae was used for the same purpose, again using formu-lae in Auerbach (2011). The only alteration in proceduresfrom that of Auerbach, 2011, was that we did estimatemissing S1 heights from the total height of the presacralvertebral column. We found no effect of sex on this esti-mation, so used a combined-sex formula (all dimensionsin millimeter):

ð3Þ ðcombined sex; n¼ 997Þ : S1 height¼ presacral height

30:0458þ 10:2; %SEE¼ 7:4%:

This allowed an additional 86 individuals (17%) to beincluded in our total sample.Following the recommendations of Raxter and Ruff

(2010), no adjustment for congenitally missing oradditional vertebrae was made, except that when indi-viduals possessed six sacral vertebrae and the normalnumber of presacral vertebrae estimated stature wasincreased by 0.8% (see Raxter and Ruff, 2010 for discus-sion).After estimation of missing elements (if necessary), all

element lengths or heights were added together to obtainskeletal height, which was then converted to living stat-ure (including soft tissue) using Eq. (1) in Raxter et al.(2006), which includes an age term. The age term is nec-essary because of differences in age structure betweenthe reference sample used to derive this equation andmost archeological samples (Raxter et al., 2007). Forspecimens with estimated ages, midpoints of age rangesfor each individual, determined as described above, wereused in the equation.

Body mass estimation

Individual body masses were determined from biiliacbreadth and reconstructed stature using sex-specific for-mulae (Ruff et al., 2005). These are based on a world-wide sample of modern human populations, including anumber of European samples (Ruff, 1994; Ruff et al.,2005). Biiliac breadth was determined after rearticulat-ing coxal bones and the sacrum. Complete pelves wereavailable for about two-thirds of the total sample (759 of1,145 individuals). The remainder were missing someportions, but preserved at least a hemipelvis from whichbiiliac breadth could be estimated. For application ofbody mass estimation equations, skeletal was convertedto living biiliac breadth using a previously described for-mula (Ruff et al., 1997, 2005; Auerbach and Ruff, 2004).Anatomical reconstruction of stature was possible in 406individuals of this sample. Stature in the remainingindividuals was calculated from long bone lengths (inalmost all cases femoral) using the stature estimationformulae developed in the present study.

Statistical procedures

As noted earlier, RMA regression is used to generateprediction equations. RMA slopes can be convenientlyderived from LS slopes by dividing LS slopes by the cor-

relation coefficient (Hofman, 1988). Y-intercepts can thenbe calculated using the slope and mean x and y values(which remain the same in both LS and RMA models).Following previous conventions (e.g., Trotter and Gleser,1952; Sjøvold, 1990; Formicola and Franceschi, 1996), alldimensions used in stature estimation equations areexpressed in centimeter. For body mass estimation, fem-oral head breadth is expressed in millimeter and bodymass in kilogram.Several criteria are used to assess estimation error of

the prediction equations: the SEE; the %SEE, calculatedas (SEE/mean y) 3 100; and the percent prediction error(%PE), calculated as [(true-predicted)/predicted] 3 100(Smith, 1984). (In this case, ‘‘true’’ is the stature valueobtained using the anatomical method, and the bodymass obtained using the stature–biiliac method.) TheSEE and %SEE are measures of overall dispersion of val-ues, i.e., random error, whereas the %PE measures direc-tional bias. In evaluating differences between techniquesor geographic and temporal variability within the presentsample, directional bias (%PE) is emphasized. The RMASEEs were calculated as described in Sjøvold (1990).All analyses were carried out both within sex and for

combined-sex samples. Combined-sex analyses were per-formed both to provide equations where sex might not bedeterminable and to assess the effects of subdivision bysex on prediction accuracy (e.g., see Sjøvold, 1990).Results are compared between the temporal periods andgeographic regions shown in Table 1. Results are alsocompared with those obtained by applying several previ-ous prediction equations. For stature estimation, theseinclude Trotter and Gleser (1952) whites, Sjøvold (1990)‘‘Caucasians,’’ and Formicola and Franceschi (1996) Eu-ropean Neolithics. For body mass estimation, theyinclude equations from Ruff et al. (1991), McHenry(1992; see Ruff et al., 1997), and Grine et al. (1995). Sex-specific equations are used when available; Sjøvold’s(1990), McHenry’s (1992), and Grine et al.’s (1995) equa-tions are for pooled sex samples.Almost all statistical analyses were carried out using

SYSTAT (2009). Comparison of RMA line elevations inone analysis was performed using the program SMATR(bio.mq.edu.au/ecology/SMATR//index.html; see Wartonet al., 2006).

RESULTS

Descriptive statistics for bone lengths, femoral headbreadth, and biiliac breadth in the study samples are givenin Table 2. Dimensions are given in millimeter (unlike instature estimation equations). The size range representedin the samples is quite large, encompassing much of therange of variation found among modern humans, with theexception of very small (i.e., Pygmy) populations (e.g.,Trinkaus, 1981; Tague, 1989; Kurki, 2011).

Stature estimation

Stature estimation equations and associated statisticsare given in Table 3. A plot of stature (anatomicallyreconstructed) against femoral length in males andfemales is shown in Figure 1a,b, with both LS and RMAregression lines plotted. The above-noted tendency forLS regression to underestimate values for tall individu-als and overestimate values for short individuals is wellillustrated in these plots. The RMA regressions fit thedata scatters better at both ends of the ranges.



As commonly observed (e.g., Trotter and Gleser, 1952;Sjøvold, 1990; Formicola and Franceschi, 1996), lowerlimb bone lengths produce smaller SEEs of stature thanupper limb bone lengths, which is expected because theycontribute directly to stature (even more so in studieswhere statures were derived through anatomical recon-struction, e.g., Formicola and Franceschi, 1996 and thepresent study). Standard errors of estimate for the pres-ent study equations are generally smaller than those ofTrotter and Gleser (1952) and Sjøvold (1990) but higherthan those of Formicola and Franceschi (1996). However,SEEs given by the last authors are for LS equations, nottheir favored major axis equations, and Model II (majoraxis, RMA) SEEs would be higher (Sjøvold, 1990;Konigsberg et al., 1998).

Femoral equations. The RMA regression coefficientsfor male and female femora in Table 3 are remarkablysimilar, indicating little difference in scaling relation-ships between the sexes. The combined-sex equation pro-duces a %SEE and mean %PE across the pooled samplesimilar to that for within-sex equations. However, withinsex, use of the combined-sex equation produces slightlyhigher mean %PEs for males (20.10%) and females(20.16%) (data not shown) compared with the within-sexequations.Scatterplots of anatomically reconstructed stature

against stature predicted from maximum femoral length

using equations from the present study (Table 3) andthree previous studies are shown in Figure 2a–d. Thethree previous equations include Trotter and Gleser’s(1952) sex-specific formulae for US whites, Sjøvold’s(1990) pooled-sex RMA formula for ‘‘Caucasians,’’ andFormicola and Franceschi’s (1996) favored sex-specificmajor axis formulae for European Neolithics. Sexes aredistinguished in the plots, and a line of equivalence isshown for comparison. Table 4 gives the mean %PEs, bysex, for each of the equations.Both Trotter and Gleser’s (1952) and Sjøvold’s (1990)

equations overestimate anatomically derived stature ofthe present study sample, on average, in both sexes(Table 4, Fig. 1b,c). (Note that because of the way thatthey are calculated, negative %PEs indicate overestima-tion, and vice versa.) Formicola and Franceschi’s (1996)equations are the most accurate of the previously avail-able methods, although they still tend to slightly over-estimate anatomical stature in males and underesti-mate stature in females (Table 4). The better perform-ance of Formicola and Franceschi’s equations is notunexpected, as they were derived using a techniquesimilar to that of the present study (i.e., anatomicallyreconstructing stature) applied to European Neolithicspecimens.Figure 3a,b breaks down %PEs of the present study

femoral stature estimates by geographic region and tem-poral period. There is very little systematic bias in esti-

TABLE 3. Stature estimation equations

Bonea Region Sex n Slope Intercept r SEE %SEE %PEb

Femur All Males 268 2.72 42.85 0.907 3.21 1.94 0.02Females 233 2.69 43.56 0.875 2.92 1.87 0.04Combined 501 2.77 40.50 0.930 3.12 1.93 0.03

Tibia North Males 154 3.09 52.04 0.881 3.53 2.11 20.09Females 146 2.92 56.94 0.832 3.20 2.04 0.04Combined 300 3.13 50.11 0.913 3.46 2.14 0.01

South Males 114 2.78 60.76 0.913 3.05 1.86 0.02Females 87 3.05 49.68 0.888 2.90 1.88 20.02Combined 201 3.02 51.36 0.927 3.14 1.97 \0.01

Fem. 1 Tib. North Males 154 1.49 43.55 0.918 2.93 1.75 0.02Females 146 1.42 48.59 0.889 2.60 1.66 0.07Combined 300 1.49 43.53 0.943 2.80 1.73 20.01

South Males 114 1.40 49.68 0.930 2.74 1.67 \0.01Females 87 1.47 42.96 0.894 2.82 1.82 20.02Combined 201 1.48 43.00 0.939 2.87 1.79 0.04

Humerus All Males 265 3.83 41.42 0.825 4.34 2.62 20.04Females 228 3.38 54.60 0.770 3.94 2.52 0.08Combined 493 3.72 44.86 0.870 4.23 2.62 20.07

Radius All Males 257 4.85 47.46 0.813 4.53 2.73 20.10Females 216 4.20 63.08 0.758 4.09 2.73 \0.01Combined 473 4.46 56.94 0.866 4.32 2.68 0.07

a All dimensions maximum lengths, in cm.b [(True-predicted)/predicted] 3 100.

TABLE 2. Study sample descriptive statistics

Dimension (mm)aMales Females

n Mean SD Range n Mean SD Range

Femoral max. length 268 452.0 27.3 383.0–543.0 233 418.0 21.8 353.0–481.0Tibial max. length 268 372.4 24.6 303.0–447.0 233 342.8 19.3 279.0–413.0Humeral max. length 265 325.3 19.2 278.5–378.0 228 299.5 17.2 243.5–346.0Radial max. length 257 244.5 15.3 201.8–283.5 216 221.2 14.0 180.3–258.0Femoral head SI bd. 624 48.0 2.9 38.5–56.1 521 42.5 2.5 35.1–51.8Pelvic biiliac bd. 624 272.8 16.9 221.0–333.0 521 265.5 16.7 214.0–318.0

a See text for further description.

6 C.B. RUFF ET AL.


mates along either dimension. Regional variation in%PEs is small, with all regions averaging less than60.9% (Fig. 3a). There is no systematic latitudinal orlongitudinal variation: although both France and Italyshow slight average overestimation of stature (negative%PE), the other two more southern regions—Iberia andthe Balkans—do not, and there is no consistent east–west trend in errors. All temporal periods have mean%PEs of less than 60.7%, except for the very small (n 55) Mesolithic sample (Fig. 3b). Even in the Mesolithicsample, four of five individuals have %PEs of \1.8%.The possible slight deviation of Mesolithic specimens isdiscussed further in the Discussion section.

Tibial equations. Tibial stature estimation equationswere originally generated from the total available sam-ple (n 5 501). Errors using these (sex-specific) equations,by region, are shown in Figure 4a. There is a clear lati-tudinal trend in errors, with all northern regions exhib-iting positive %PEs and all southern regions negative%PEs (recall that the French samples are all from thesouthern half of France). As discussed in more detaillater, these trends are consistent with more general eco-geographic trends in limb proportions—relatively longerdistal limb elements, characteristic of more southernpopulations, will lead to systematic overestimation ofstature (negative %PEs), and vice versa, when using apooled sample equation based on these elements. There-fore, it is necessary to use region-specific equations whenusing the tibia to estimate stature. Here, that was doneby dividing the sample into northern and southern sub-samples, with Britain, Scandinavia, and north-centralEurope in the former, and France, Italy, Iberia, and theBalkans in the latter. These equations are given in Table3. Figure 4b shows %PEs by region after applying theregion-specific equations. All mean %PEs are now below60.5%, and there is no systematic latitudinal trend. TheFrench and Italian samples are still slightly low, similarto the pattern for femora (Fig. 3a), but this seems to bemore sample specific rather than reflective of a broad ge-ographic trend. There is no east–west trend in errors ineither comparison (Fig. 4a,b). Temporal variation in%PEs for tibial equations is shown in Figure 4c.

Although there is more overall temporal variability inerrors than with the femur (Fig. 3b), there is no cleartemporal trend, and all mean %PEs are less than 61%.The Mesolithic sample is not an outlier.No specific comparisons of %PEs between the present

study and the three primary comparative studies (Trotterand Gleser, 1952; Sjøvold, 1990; Formicola and France-schi, 1996) are carried out for the tibia here, in partbecause of differences in the specific tibial length dimen-sions used in the other studies (Sjøvold, 1990; Jantz etal., 1994; Formicola and Franceschi, 1996), and alsobecause no other studies have reported region-specificequations. As with the femur, use of the combined-sexformulae in Table 3 results in higher %PEs within sexcompared with the sex-specific formulae (northern males,20.18%, northern females, 20.17%; southern males0.34%, southern females, 20.44%; data not shown).Table 3 also includes stature estimation equations for

femoral 1 tibial lengths. Because of the geographic vari-ation in relative tibial length, these formulae were alsodeveloped separately for northern and southern subsam-ples. The %PEs by region and temporal period usingthese formulae are all �1.0% (data not shown).

Upper limb equations. Humeral and radial %PEs forstature estimation, by region and time period, are shownin Figure 5a–d. Almost all mean %PEs are within 61%.There are no apparent general geographic or temporaltrends in the errors, although there is a slight tendencyfor earlier time periods to show more positive %PEs forthe humerus, especially in the Neolithic (Fig. 5b). How-ever, this pattern is not evident for the radius (Fig. 5d).Latitudinal variation for the radius (Fig. 5c) is not con-sistent as in the tibia (Fig. 4a), indicating much lessmarked ecogeographic variation in the distal element ofthe upper limb (also see Discussion); thus, regional ver-sions of the radius formulae were not developed.Comparisons of %PEs for the humerus and radius

between the present study and the three comparativestudies (Trotter and Gleser, 1952; Sjøvold, 1990; Formi-cola and Franceschi, 1996) yield results very similar tothose shown in Table 4 for the femur: both Trotter andGleser’s (1952) and Sjøvold’s (1990) formulae consistently

Fig. 1. Anatomically reconstructed stature against maximum femoral length in the study sample: (a) males and (b) females.Solid lines are LS regressions through the data; dashed lines are RMA regressions.



overestimate stature, by [1.5% on average in almost allcomparisons, whereas Formicola and Francheschi’s(1996) formulae perform somewhat better but still pro-duce average underestimate or overestimate of between0.5 and 2.1% (data not shown). Again, combined-sex for-mulae generally produce higher mean %PEs within sexthan sex-specific equations, especially for females (malehumerus, 20.04%, female humerus, 20.19%; male ra-dius, 20.09%, female radius, 0.26%; data not shown).

Body mass estimation

Body mass estimation equations are given in Table 5.Plots of body mass against femoral head breadth inmales and females are given in Figure 6a,b, along withLS and RMA regression lines. Again, as with statureprediction, the RMA lines fit the data scatters better.Percent standard errors of estimate are higher thanwith stature estimation equations, as expected, but arelower than those reported in another study that included

individual data (Ruff et al., 1991). (Of course, because itwas based on living humans, the previous study moreaccurately incorporated errors due to soft tissue varia-tion.) Females have lower body mass PEs than malesusing all criteria. The combined-sex formula is interme-diate in this respect, although again, as with statureestimation equations, mean %PEs within sex using thecombined-sex formula are higher than that those usingsex-specific formulae, especially for females (males,20.78% and females, 2.30%).Because femoral head breadth and body mass are

dimensionally different, it is possible that power ratherthan linear relationships would fit the data better. How-ever, correlations and SEEs following logarithmic trans-formation were virtually identical to those for the linearequations (data not shown). This is not unexpected fol-lowing theoretical predictions (Sjøvold, 1990; Albrecht etal., 1993) and previous empirical results (Ruff et al.,1991; Grine et al., 1995) for within-species analyses.Therefore, only linear equations are given.

Fig. 2. Anatomically reconstructed stature against stature predicted from maximum femoral length in the study sample: (a)present study equations, (b) Trotter and Gleser (1952) white equations, (c) Sjøvold (1990) ‘‘Caucasian’’ equation, and (d) Formicolaand Franceschi (1996) Neolithic Europeans, major axis equations. All estimates from sex-specific equations, except Sjøvold (1990).Crosses: males; circles: females. Lines indicate identity.

8 C.B. RUFF ET AL.


Scatterplots of body mass calculated from stature andbiiliac breadth (Ruff et al., 2005) against body mass pre-dicted from femoral head breadth using the formulaedeveloped in the present study and three sets of previ-ously available formulae (Ruff et al., 1991; McHenry,1992; Grine et al., 1995) are shown in Figure 7a–d. Asso-ciated mean %PEs are given in Table 6. Because PEs forthe different equations have previously been shown tovary by body size (Auerbach and Ruff, 2004; Kurki et al.,2010), in addition to total sample and sex-specific %PEs,%PEs for individuals below and above the mean samplebody mass (63 kg) are shown in Table 6. Also, becausedifferent combinations (averages) of femoral head bodymass estimation equations have been used in past stud-ies, in part based on size range of the target sample(Ruff, 2010; Pomeroy and Stock, 2012), results are givenin Table 6 for the average of all three previous equationsas well as the average of the Ruff et al.’s (1991) andGrine et al.’ (1995) equations. The latter two equationsare based on medium-to-large modern humans, whereasMcHenry’s (1992) sample included very small humans(Pygmies and Khoisan; for details, see Auerbach andRuff, 2004). Only Ruff et al. (1991) provided sex-specificestimation equations.All previous equations and averages of equations,

except for McHenry (1992), consistently overestimatebody mass in the sample as a whole and within sex

(Table 6, Fig. 7c,d). They also perform poorly amongsmaller adults but better in larger adults (Table 6). Per-haps not surprisingly, McHenry’s equation works verywell in smaller adults but has the largest average %PEamong larger adults. The apparent size effect on resultsis not simply sex related, because McHenry’s equationworks better for males than for females. Thus, all previ-ously available body mass estimation equations haveshortcomings when applied to the present sample, whichwas a major rationale for developing new equationsbased on the present sample itself.Figure 8a,b shows %PEs of body mass subdivided geo-

graphically and temporally. There is no apparent pat-terning to the variation, and all subdivisions averagewithin 64% directional bias, with the Mesolithic sampleshowing the largest bias (4.0% mean overestimation).

DISCUSSION

Previously available methods for estimating body sizein European skeletal samples are subject to a number oflimitations, including possible mismatching of body pro-portions in reference and target samples and restrictionof estimation formulae to a particular time period and/orregion. Several previously available equations exhibitsubstantial biases when applied to the present studysample. The new equations given here provide an alter-native means for estimating stature and body mass andappear to be broadly applicable to European Holocenepopulations. This does not, of course, argue against de-velopment of additional equations for specific popula-tions, when possible (e.g., Vercellotti et al., 2009). How-ever, in cases where this is not feasible, the presentequations perhaps provide the most viable option.

Geographic and temporal variation

The only systematic effect of geography found herewas on stature estimation from tibial length, where alatitudinal gradient in directional bias was observed. Asshown in Figure 9, populations from southern Europe,

Fig. 3. Box plots of %PE of stature ([(true-predicted)/predicted] 3 100) estimated from maximum femoral length by:(a) geographic region and (b) temporal period.

TABLE 4. Average %PEs for estimation of stature (determinedfrom anatomical reconstruction) from femoral maximum length

using present and previous study equations

Equation source

Percent predictionerrora

Males Females

Present study 0.02 0.04Trotter and Gleser (1958), whites 21.87 20.85Sjøvold (1990), ‘‘Caucasians’’ 21.77 22.42Formicola and Franceschi (1996), MA 20.89 0.57

a [(True-predicted)/predicted] 3 100.



i.e., the circum-Mediterranean region (south of about 468latitude), have relatively longer tibiae than populationsfrom northern Europe, a trend found in all time periods(Niskanen et al., 2012). This leads to overestimation ofstature in southern regions and underestimation innorthern regions if a common formula is used. Thus,when using the tibia to estimate stature, different equa-tions are necessary for the two regions. This result is notunexpected, as distal limb lengthening in warmer cli-mates (or shortening in colder climates) is part of a moregeneral ecogeographic cline among living and earlierhumans (Trinkaus, 1981; Ruff, 1994). Although thisoccurs in both the lower and upper limbs, variabilitybetween populations in relative tibial length is greaterthan that in relative radial length (Holliday, 1997, 1999;Holliday and Ruff, 2001). This may explain why the ra-

dius did not show as marked or geographically consist-ent trends in directional bias.Recent migrational patterns should be taken into

account when considering application of the ‘‘southern’’or ‘‘northern’’ tibial stature estimation equations, as an-cestral linear body proportions may be retained for a pe-riod of time (Trinkaus, 1981; Holliday, 1997). However,the timing and patterning of change in proportions fol-lowing migration to a new environment is complex andmultifactorial (Holliday, 1997; Bogin et al., 2002). Whenfeasible, assessing tibial length to anatomically recon-structed stature proportions in a subset of a sample canprovide some guidance. The equations given in the legendto Figure 9 can be used to calculate tibial length from an-atomical stature assuming ‘‘northern’’ and ‘‘southern’’proportions and then compared with actual tibial lengths

Fig. 4. Box plots of %PE of stature ([(true-predicted)/predicted] 3 100) estimated from maximum tibial length by: (a) geographicregion, using pooled region equations, (b) geographic region, using northern and southern equations (see text), and (c) temporalperiod, using northern and southern equations.

10 C.B. RUFF ET AL.


to identify the best fit. There is a large degree of individ-ual overlap in proportions (Fig. 9); however, samplemeans should show less variation. Using the femurrather than the tibia to estimate stature may also help tominimize this problem (although also see below).Temporal variation in PEs for stature or body mass

estimates showed no consistent trends. However, theMesolithic sample showed the largest %PE for stature,using femoral length (underestimated by an average of

1.7%), and the largest %PE for body mass (overestimatedby an average of 4.0%). Because most (13 of 16) of theMesolithic specimens included in the body mass estima-tion analyses had statures estimated from our statureformulae (in all but one case from the femur), ratherthan anatomically reconstructed statures, these tworesults are concordant: underestimation of stature willlead to underestimation of body mass using the stature–biiliac breadth method and, therefore, ‘‘overestimation’’of body mass using the femoral head equations derivedfrom the total sample. This suggests some possible slightdifferences in linear body proportions in the Mesolithicsample compared with the overall sample, specifically, aslightly shorter femur relative to stature. In fact, femurlength relative to trunk length in European Mesolithicsis slightly less than that in modern Europeans (Holliday,1997; his modern samples were all Medieval or Romano-British). Relative tibial length, however, is not shorter inMesolithics (Holliday, 1997; also see present results);

Fig. 5. Box plots of %PE of stature ([(true-predicted)/predicted] 3 100) estimated from maximum humeral and radial lengths:(a) humerus, by geographic region; (b) humerus, by temporal period; (c) radius, by geographic region; and (d) radius, by temporalperiod.

TABLE 5. Body mass (kg) estimation equations from femoralhead superoinferior breadth (mm)

Sex n Slope Intercept r SEE %SEE %PEa

Males 624 2.80 266.70 0.636 6.84 10.11 0.68Females 521 2.18 235.81 0.671 4.44 7.82 0.34Combined 1,145 2.30 241.72 0.793 5.67 9.04 0.62




Fig. 7. Body mass calculated from stature and biiliac breadth against body mass estimated from femoral head superoinferiorbreadth using three previous and the present study femoral head equations: (a) present study equations; (b) McHenry (1992);(c) Ruff et al. (1991); and (d) Grine et al. (1995). Crosses: males; circles: females. Lines indicate identity.

Fig. 6. Body mass calculated from stature and biiliac breadth against femoral head superoinferior breadth in the study sample:(a) males and (b) females. Solid lines are LS regressions through the data; dashed lines are RMA regressions.

thus, crural indices (tibia/femur length) are greater inMesolithics than in more recent Europeans (Holliday,1997, 1999). This intralimb proportional difference inMesolithics may be a remnant from earlier, i.e., UpperPaleolithic populations (Trinkaus, 1981; Ruff, 1994; Hol-liday, 1997, 1999). Formicola and Franceschi (1996) alsoreported a slight underestimation of stature in EuropeanMesolithics using their major axis formula derived froma Neolithic sample. Their results were derived from anaverage of femoral and tibial estimates but would beconsistent with the present results (little directional biasfor the tibia and a larger negative one for the femur).The Mesolithic sample included here with anatomicallyderived statures is very small (n 5 5), however, as wasthat of Formicola and Franceschi (also n 5 5; there wasno overlap between specimens in the two samples), sothis possible differentiation from later European Holo-cene samples must remain tentative until larger samplesare analyzed. In any event, the average directional biasin stature estimates is still relatively small—under 2%.

Error in ‘‘true’’ stature and body mass

The effect of a possible bias in stature estimation onbody mass estimation in the Mesolithic sample under-scores a possible weakness in the method used here toderive body mass prediction equations, namely, assum-

ing that the stature–biiliac equations accurately esti-mate body mass. In almost two-thirds of the body massestimation sample (739/1,145 individuals), stature wasestimated using our derived long bone equations ratherthan being anatomically reconstructed. Body mass esti-mation equations were also developed for only the subsetof 406 individuals with anatomically reconstructed stat-ures and are presented in Supporting Information TableS3. As shown there, %PEs are slightly smaller thanthose for the equations based on the larger sample(0.33% for males, 0.24% for females, and 0.28% for com-bined sexes). As might be expected, though, this moreselect sample is somewhat less representative of differ-ent temporal periods, with relatively fewer individualsfrom the three earliest periods (55 [14%], compared with259 [23%] for the larger sample), and relatively morefrom the two most recent periods (103 [25%], comparedwith 188 [16%] for the larger sample). Therefore, weadvocate using the equations in Table 5, but the otherequations are available for those who prefer them. Ana-tomical reconstruction of stature is not without erroritself, but errors using this method are comparativelysmall and, perhaps most importantly, do not show direc-tional bias on an individual or populational basis (Raxteret al., 2006; Maijanen, 2009).Of course, even if stature and living biiliac breadth

are known exactly, there is still some error associated

Fig. 8. Box plots of %PE of body mass ([(true-predicted)/predicted] 3 100) estimated from femoral head breadth by:(a) geographic region and (b) temporal period.

TABLE 6. Average %PEs for estimation of body mass (determined from stature and biiliac breadth) from femoral head breadthusing present and previous study equations

Equation source

Percent prediction errora

All Males Females \63 kg �63 kg

Present study 0.53 0.68 0.34 21.36 2.87McHenry (1992) 1.77 0.48 3.31 0.23 3.68Ruff et al. (1991) 23.94 21.49 26.88 27.54 0.52Grine et al. (1995) 25.57 26.23 24.77 27.49 23.18Mean, three previous 22.72 22.50 22.97 25.10 0.25Mean, Ruff et al. (1991) and Grine et al. (1995) 24.80 23.92 25.84 27.55 21.38




with body mass estimated from these parameters (Ruff,2000; Ruff et al., 2005). This might argue in favor ofusing one of the other available femoral head estimationequations, which were based on modern human samples,some of which had associated body masses (Ruff et al.,1991; McHenry, 1992; Grine et al., 1995). However, eachof these samples had some limitations, including a smallnumber of data points, some of which included estimatedbody masses (McHenry, 1992; Grine et al., 1995 andJungers, personal communication) and corrections forincreased adiposity in a living urban sample (Ruff et al.,1991). They all also produce variable biases (comparedwith stature–biiliac estimates) when applied to the pres-ent study sample. Using the present study sample itselfto derive body mass estimation equations has theadvantage of using a much larger sample size, and onewhich is almost certainly more representative of therange of body size and shape among Holocene Europeans(e.g., see Table 2). Even the mismatch between femoralhead and stature–biiliac estimates of body mass in theMesolithic sample is reassuring in one sense, in that thefemoral head equations correctly identified the probableunderestimation of stature in this sample.

Sex and age effects

Pooled sex equations produce random and directionalerrors that are similar to those for sex-specific equations,when averaged over the entire sample. However, whenanalyzed within sex, directional bias is always largerusing the combined-sex equations (males and females of-ten show different directions of bias, which cancel outwhen errors are averaged). Thus, sex-specific equationsshould be used when possible; however, combined-sexequations produce reasonable results when sex cannotbe determined. These results, and the remarkably simi-lar RMA regression coefficients in males and females forfemoral prediction of stature, give some support to theview of a general commonality in limb bone length to

stature scaling in the sexes (Sjøvold, 1990), at least forthe femur. However, some subtle sex differences in allo-metric scaling of the limbs have also been demonstrated(Sylvester et al., 2008; Auerbach and Sylvester, 2011),giving further reason to use sex-specific methods of bodysize reconstruction when possible. As noted above, thestature–biiliac method of body mass estimation shouldonly use sex-specific equations, but this limitation doesnot strictly apply to the femoral head equationspresented here.Stature declines with age in adults, primarily because

of compression of vertebral discs and vertebral bodies(Friedlaender et al., 1977). Because mathematical recon-structions of stature from long bones do not directly takethis into consideration, some adjustment of stature esti-mates for age may be warranted. On the basis of thedata from their own sample (Trotter and Gleser, 1951),Trotter and Gleser (1952) recommended reducing statureestimates by 0.06 cm/year after 30 years to account forage-related changes. In fact, reductions in stature withaging are more complex than this, following a quadraticcurve that is steeper among women (Cline et al., 1989;Chandler and Bock, 1991; Sorkin et al., 1999a,b).Whether any age correction should be applied to esti-mates derived from formulae based on anatomical recon-structions of stature, like those of the present study, isdebatable (Raxter et al., 2008; Vercellotti et al., 2009).The anatomical stature reconstruction formula #1 ofRaxter et al. (2006) already includes an age term, whichshould take into account the skeletal component of age-related statural loss (see original reference for discus-sion). However, as in other such studies based on ana-tomical reconstructions, the present study equationswere derived for the complete, i.e., age-combined sample.Thus, it is still possible that PEs vary systematically byage.Figure 10a,b plots %PEs of stature against age in

males and females of the present study, with staturederived from the femoral length equations. Femalesshow a significant linear decline in %PE with age (r 50.210, P \ 0.001). The male %PEs are better fit by aquadratic equation, although the regression is only nearsignificant (r 5 0.135, P 5 0.086). (In both cases, theAkaike Information Criterion was used to choose thebest-fitting model.) In both sexes, then, there is an over-estimation of stature (negative %PE) among olderadults, although this trend is apparent earlier andreaches a higher level of statistical significance infemales. To a large extent, these findings parallel thosereported in studies of living humans (see referencesabove). The effects on stature estimation are relativelysmall, though, with average directional errors of \2%among our oldest adults (Fig. 10). The low frequency ofvery old adults (or, at least, adults that can be agedaccurately) in archeological collections also reduces thepractical effectiveness of any such age adjustment. (Thegreat majority of the individuals aged as 60 years orolder in the present study sample were from recentosteological collections of known age.) Of course, theresults shown in Figure 10 do not include any possibleadditional stature loss due to soft tissue reduction withaging, but it is not possible to estimate the magnitude ofthis loss in the present study sample or in studies of liv-ing samples.Therefore, we do not advocate applying an age adjust-

ment factor to stature estimates derived from the pres-ent study formulae. Whether ‘‘maximal’’ stature (i.e.,

Fig. 9. Maximum tibial length relative to stature in north-ern (filled squares and solid line) and southern (open squaresand dashed line) samples (lines are RMA regressions). Differ-ence between line elevations is significant at P < 0.001. RMAequations are as follows: southern: tibia length 5 0.331 3 stat-ure 2 17.0; northern: tibia length 5 0.319 3 stature 2 15.7.

14 C.B. RUFF ET AL.


stature achieved in early adulthood) or actual stature isthe best parameter to examine (e.g., Niewenweg et al.,2003; Maijanen and Niskanen, 2010) is a different issuethat will depend on the particular aims of an investiga-tion. When reconstructing anatomical stature, though,we do advocate using the formula with an age term (#1)in Raxter et al. (2006), given the large difference in agestructure between the reference sample and most arche-ological samples (Raxter et al., 2007).As would be expected, we found no effect of age on any

of the body mass estimation errors in the present study.

CONCLUSIONS

New equations for estimating stature from long bonelengths and body mass from femoral head breadth aredeveloped from a large sample of European skeletonsspanning the Holocene and much of the continent, fromFinland and the Balkans to Britain and the Iberian Pen-insula (n 5 501 for stature and n 5 1,145 for bodymass). Stature is determined through anatomical recon-struction and body mass from stature and biiliacbreadth. Average PEs are smaller than in previouslyavailable methods. Based on the patterning of PEs, thesame equations appear to be broadly applicable acrossdifferent geographic regions and temporal periods. Theone exception is stature estimation from tibial length,where northern (above about 468 N. latitude) and south-ern equations are necessary because of relatively longertibiae in southern populations, part of a general ecogeo-graphic trend among humans. There is also a suggestionof slightly different linear scaling in our small Mesolithicsample, but this will need to be confirmed in larger sam-ples.Although these equations should be generally applica-

ble to Holocene European skeletal material, similar anal-yses of individuals or samples, when feasible, will helpto further test the methods and their appropriateness inspecific cases. It is hoped that the present study willserve as a stimulus for future investigations of body sizeprediction from skeletal remains, both in Europe andother regions.

ACKNOWLEDGMENTS

The authors thank Trang Diem Vu, Sarah Reedy,Quan Tran, Andrew Merriweather, Juho-Antti Junno,Anna-Kaisa Salmi, Tiina Vare, Rosa Vilkama, JaroslavRoman, and Petra Spevackova for help in collecting and/or processing of data. They also thank all of the peoplewho provided access to skeletal collections and whohelped in other ways to facilitate data acquisition:Andrew Chamberlain, Rob Kruszynski, Jay Stock, Mer-cedes Okumura, Jane Ellis-Schon, Jacqueline McKinley,Lisa Webb, Jillian Greenaway, Alison Brookes, Jo Buck-berry, Chris Knusel, Horst Bruchhaus, Ronny Bindl,Hugo Cardoso, Sylvia Jimenez-Brobeil, Maria DoloresGarralda, Michele Morgan, Clive Bonsall, Adina Boro-neant, Alexandru Vulpe, Monica Zavattaro, Elsa Pac-ciani, Fulvia Lo Schiavo, Maria Giovanna Belcastro,Alessandro Riga, Nico Radi, Giorgio Manzi, MaryanneTafuri, Pascal Murail, Patrice Courtaud, Dominique Cas-tex, Frederik Leterle, Emilie Thomas, Aurore Schmitt,Aurore Lambert, Sandy Parmentier, Alessandro Canci,Gino Fornaciari, Davide Caramella, Jan Stora, AnnaKjellstrom, Petra Molnar, Niels Lynnerup, Pia Bennike,Leena Drenzel, Torbjorn Ahlstrom, Per Karsten, BerndGerlach, Lars Larsson, Petr Veleminsky, Maria Teschler-Nicola, and Anna Pankowska.

LITERATURE CITED

Aiello LC. 1992. Allometry and the analysis of size and shape inhuman evolution. J Hum Evol 22:127–148.

Albrecht GH, Gelvin BR, Hartman SE. 1993. Ratios as a sizeadjustment in morphometrics. Am J Phys Anthropol 91:441–468.

Arsuaga J-L, Lorenzo C, Carretero J-M, Gracia A, Martinez I,Garcia N, Bermudez de Castro J-M, Carbonell E. 1999. Acomplete human pelvis from the Middle Pleistocene of Spain.Nature 399:255–258.

Auerbach BM. 2011. Methods for estimating missing humanskeletal element osteometric dimensions employed in the re-vised Fully technique for estimating stature. Am J PhysAnthropol 145:67–80.

Fig. 10. Percent prediction error of stature ([(true-predicted)/predicted] 3 100) against age in: (a) males and (b) females.Quadratic regression equation fit through males; linear regression through females (both LSs) (see text).



Auerbach BM, Ruff CB. 2004. Human body mass estimation: acomparison of "morphometric" and "mechanical" methods. AmJ Phys Anthropol 125:331–342.

Auerbach BM, Ruff CB. 2006. Limb bone bilateral asymmetry:variability and commonality among modern humans. J HumEvol 50:203–218.

Auerbach BM, Ruff CB. 2010. Stature estimation formulae forindigenous North American populations. Am J Phys Anthro-pol 141:190–207.

Auerbach BM, Sylvester AD. 2011. Allometry and apparent par-adoxes in human limb proportions: implications for scalingfactors. Am J Phys Anthropol 144:382–391.

Bogin B, Keep R. 1999. Eight thousand years of economic andpolitical history in Latin America revealed by anthropometry.Ann Hum Biol 26:333–351.

Bogin B, Smith P, Orden AB, Varela Silva MI, Loucky J. 2002.Rapid change in height and body proportions of Maya Ameri-can children. Am J Hum Biol 14:753–761.

Brooks S, Suchey JM. 1990. Skeletal age determination basedon the os pubis: a comparison of the Ascadi-Nemeskeri andSuchey-Brooks methods. Hum Evol 5:227–238.

Bruzek J. 2002. A method for visual determination of sex, usingthe human hip bone. Am J Phys Anthropol 117:157–168.

Buckberry JL, Chamberlain AT. 2002. Age estimation from theauricular surface of the ilium: a revised method. Am J PhysAnthropol 119:231–239.

Buikstra JE, Ubelaker DH. 1994. Standards for data collectionfrom human skeletal remains. Fayetteville, AR: ArkansasArchaeological Survey.

Chandler PJ, Bock RD. 1991. Age changes in adult stature:trend estimation from mixed longitudinal data. Ann Hum Biol18:433–440.

Cline MG, Meredith KE, Boyer JT, Burrows B. 1989. Decline ofheight with age in adults in a general population sample: esti-mating maximum height and distinguishing birth cohorteffects from actual loss of stature with aging. Hum Biol61:415–425.

Cohen MN, Crane-Kramer GMM, editors. 2007. Ancient health:skeletal indicators of agricultural and economic intensifica-tion. Gainesville: University Press of Florida.

Duyar I, Pelin C. 2003. Body height estimation based on tibialength in different stature groups. Am J Phys Anthropol122:23–27.

Falys CG, Schutkowski H, Weston DA. 2006. Auricular surfaceaging: worse than expected? A test of the revised method on adocumented historic skeletal assemblage. Am J Phys Anthro-pol 130:508–513.

Feldesman MR, Lundy JK. 1988. Stature estimates for some Afri-can Plio-Pleistocene fossil hominids. J HumEvol 17:583–596.

Formicola V. 1993. Stature reconstruction from long bones inancient population samples: an approach to the problem of itsreliability. Am J Phys Anthropol 90:351–358.

Formicola V, Franceschi M. 1996. Regression equations for esti-mating stature from long bones of early holocene Europeansamples. Am J Phys Anthropol 100:83–88.

Frayer DW. 1984. Biological and cultural change in the Euro-pean Late Pleistocene and Early Holocene. In: Smith FH,Spencer F, editors. The origins of modern humans: a worldsurvey of the fossil evidence. New York: Wiley-Liss. p211–250.

Friedlaender JS, Costa PT Jr, Bosse R, Ellis E, Rhoads JG,Stoudt HW. 1977. Longitudinal physique changes amonghealthy white veterans at Boston. Hum Biol 49:541–558.

Fully G. 1956. Une nouvelle methode de determination de lataille. Ann Med Legale 35:266–273.

Giannecchini M, Moggi-Cecchi J. 2008. Stature in archeologicalsamples from central Italy: methodological issues and dia-chronic changes. Am J Phys Anthropol 135:284–292.

Grine FE, Jungers WL, Tobias PV, Pearson OM. 1995. FossilHomo femur from Berg Aukas, northern Namibia. Am J PhysAnthropol 97:151–185.

Hanson CL. 1992. Population-specific stature reconstruction forMedieval Trondheim, Norway. Int J Osteoarchaeol 2:289–295.

Hofman MA. 1988. Allometric scaling in paleontology: a criticalsurvey. Hum Evol 3:177–188.

Holliday TW. 1997. Body proportions in Late Pleistocene Europeand modern human origins. J Hum Evol 32:423–447.

Holliday TW. 1999. Brachial and crural indices of EuropeanLate Upper Paleolithic and Mesolithic humans. J Hum Evol36:549–566.

Holliday TW, Ruff CB. 1997. Ecogeographic patterning and stat-ure prediction in fossil hominids: comment on Feldesman andFountain. Am J Phys Anthropol 103:137–140.

Holliday TW, Ruff CB. 2001. Relative variation in human proxi-mal and distal limb segment lengths. Am J Phys Anthropol116:26–33.

Jantz RL, Hunt DR, Meadows L. 1994. Maximum length of thetibia: how did Trotter measure it? Am J Phys Anthropol93:525–528.

Konigsberg LW, Hens SM, Jantz LM, Jungers WL. 1998. Stat-ure estimation and calibration: Bayesian and maximum likeli-hood perspectives in physical anthropology. Yearb PhysAnthropol 41:65–92.

Krogman WM, Iscan MY. 1986. The human skeleton in forensicmedicine. Springfield, IL: Charles C. Thomas.

Kurki HK. 2011. Pelvic dimorphism in relation to body size andbody size dimorphism in humans. J Hum Evol 61:631–643.

Kurki HK, Ginter JK, Stock JT, Pfeiffer S. 2010. Body size esti-mation of small-bodied humans: applicability of current meth-ods. Am J Phys Anthropol 141:169–180.

Maijanen H. 2009. Testing anatomical methods for stature esti-mation on individuals from the W. M. Bass Donated SkeletalCollection. J Forensic Sci 54:746–752.

Maijanen H, Niskanen M. 2006. Comparing stature-estimationmethods on Medieval inhabitants of Westerhus, Sweden. Fen-noscandia Archaeol 23:37–46.

Maijanen H, Niskanen M. 2010. New regression equations forstature estimation for Medieval Scandinavians. Int J Osteoar-chaeol 20:472–480.

McHenry HM. 1992. Body size and proportions in early homi-nids. Am J Phys Anthropol 87:407–431.

Meiklejohn C, Babb J. 2011. Long bone length, stature and timein the European Late Pleistocene and Early Holocene. In: Pin-hasi R, Stock JT, editors. Human bioarchaeology of the transi-tion to agriculture. Chicester: Wiley-Blackwell. p153–175.

Miles AE. 1963. The dentition in the assessment of individualage in skeletal material. Dent Anthropol 5:191–208.Milisauskas S, editor. 2002. European prehistory: a survey.New York: Kluwer Academic/Plenum.

Niewenweg R, Smit ML, Walenkamp MJ, Wit JM. 2003. Adultheight corrected for shrinking and secular trend. Ann HumBiol 30:563–569.

Niskanen M, Ruff C, Holt B, Sladek V, Berner M, Garvin H,Garofalo E, Tompkins D, Junno J-A, Niinimaki S, Salmi A-K,Salo K, Heikkila T, Vilkama R. 2012. Temporal trends and re-gional differences in body size and shape of Europeans fromthe Late Pleistocene to recent times (abstract). Am J PhysAnthropol Suppl 54:224.

Pomeroy E, Stock JT. 2012. Estimation of stature and bodymass from the skeleton among coastal and mid-altitudeAndean populations. Am J Phys Anthropol 147:264–279.

Raxter MH, Auerbach BM, Ruff CB. 2006. Revision of the Fullytechnique for estimating statures. Am J Phys Anthropol130:374–384.

Raxter MH, Ruff CB. 2010. The effect of vertebral numericalvariation on anatomical stature estimates. J Forensic Sci55:464–466.

Raxter MH, Ruff CB, Auerbach BM. 2007. Technical note: re-vised Fully stature estimation technique. Am J Phys Anthro-pol 133:817–818.

Raxter MH, Ruff CB, Azab A, Erfan M, Soliman M, El-Sawaf A.2008. Stature estimation in ancient Egyptians: a new tech-nique based on anatomical reconstruction of stature. Am JPhys Anthropol 136:147–155.

Rosenberg KR, Lu Z, Ruff CB. 2006. Body size, body proportionsand encephalization in a Middle Pleistocene archaic humanfrom northern China. Proc Natl Acad Sci USA 103:3552–3556.

Ruff CB. 1994. Morphological adaptation to climate in modernand fossil hominids. Yearb Phys Anthropol 37:65–107.

16 C.B. RUFF ET AL.


Ruff CB. 2000. Body mass prediction from skeletal frame size inelite athletes. Am J Phys Anthropol 113:507–517.

Ruff CB. 2002. Variation in human body size and shape. AnnRev Anthropol 31:211–232.

Ruff CB. 2010. Body size and body shape in early hominins:implications of the Gona pelvis. J Hum Evol 58:166–178.

Ruff CB, Holt BM, Niskanen M, Sladek V. 2012. Symposium: onthe verge of modernity: skeletal adaptation in recent Euro-peans. Portland, OR: American Association of PhysicalAnthropologists.

Ruff CB, Holt BM, Sladek V, Berner M, Murphy WA, Nedden Dz,Seidler H, Reicheis W. 2006. Body size, body shape, and longbone strength of the Tyrolean iceman. J HumEvol 51:91–101.

Ruff CB, Niskanen M, Junno JA, Jamison P. 2005. Body massprediction from stature and bi-iliac breadth in two high lati-tude populations, with application to earlier higher latitudehumans. J Hum Evol 48:381–392.

Ruff CB, Scott WW, Liu AY-C. 1991. Articular and diaphysealremodeling of the proximal femur with changes in body massin adults. Am J Phys Anthropol 86:397–413.

Ruff CB, Trinkaus E, Holliday TW. 1997. Body mass andencephalization in Pleistocene Homo. Nature 387:173–176.

Ruff CB, Trinkaus E, Holliday TW. 2002. Body proportions andsize. In: Zilhao J, Trinkaus E, editors. Portrait of the artist asa child: the Gravettian human skeleton from the Abrigo doLagar Velho and its archaeological context. Lisbon: InstitutoPortugues de Arqueologia. p365–391.

Sciulli PW, Hetland BM. 2007. Stature estimation for prehis-toric Ohio Valley Native American populations based on revi-sions to the Fully technique. Archaeol East N Am 35:105–113.

Sciulli PW, Schneider KN, Mahaney MC. 1990. Stature estima-tion in prehistoric Native Americans of Ohio. Am J PhysAnthropol 83:275–280.

Shin DH, Oh CS, Kim YS, Hwang YI. 2012. Ancient-to-modernsecular changes in Korean stature. Am J Phys Anthropol147:433–442.

Sjøvold T. 1990. Estimation of stature from long bones utilizingthe line of organic correlation. Hum Evol 5:431–447.

Sladek V, Berner M, Sailer R. 2006. Mobility in Central Euro-pean Late Eneolithic and Early Bronze Age: femoral cross-sec-tional geometry. Am J Phys Anthropol 130:320–332.

Smith P, Horowitz LK. 1984. Archaeological and skeletal evi-dence for dietary change during the Late Pleistocene/EarlyHolocene in the Levant. In: Cohen MN, Armelagos GJ, edi-tors. Paleopathology at the origins of agriculture. Orlando:Academic Press. p101–136.

Smith RJ. 1984. Allometric scaling in comparative biology: prob-lems of concept and method. Am J Physiol 246:R152–R160.

Sorkin JD, Muller DC, Andres R. 1999a. Longitudinal change inheight of men and women: implications for interpretation ofthe body mass index: the Baltimore Longitudinal Study ofAging. Am J Epidemiol 150:969–977.

Sorkin JD, Muller DC, Andres R. 1999b. Longitudinal change inthe heights of men and women: consequential effects on bodymass index. Epidemiol Rev 21:247–260.

Steckel RH, Rose JC, editors. 2002. The backbone of history:health and nutrition in the Western Hemisphere. Cambridge:Cambridge University Press.

Stock J, Pfeiffer S. 2001. Linking structural variability in longbone diaphyses to habitual behaviors: foragers from thesouthern African Later Stone Age and the Andaman Islands.Am J Phys Anthropol 115:337–348.

Sylvester AD, Kramer PA, Jungers WL. 2008. Modernhumans are not (quite) isometric. Am J Phys Anthropol137:371–383.

SYSTAT. 2009. Chicago: SYSTAT Software, Inc.Tague RG. 1989. Variation in pelvic size between males and

females. Am J Phys Anthropol 80:59–71.Trinkaus E. 1981. Neanderthal limb proportions and cold adap-

tation. In: Stringer CB, editor. Aspects of human evolution.London: Taylor and Francis. p187–224.

Trotter M, Gleser G. 1951. The effect of ageing on stature. Am JPhys Anthropol 9:311–324.

Trotter M, Gleser GC. 1952. Estimation of stature from longbones of American whites and Negroes. Am J Phys Anthropol10:463–514.

Trotter M, Gleser GC. 1958. A re-evaluation of estimation ofstature based on measurements of stature taken during lifeand of long bones after death. Am J Phys Anthropol 16:79–123.

Vercellotti G, Agnew AM, Justus HM, Sciulli PW. 2009. Statureestimation in an early medieval (XI-XII c.) Polish population:testing the accuracy of regression equations in a bioarcheolog-ical sample. Am J Phys Anthropol 140:135–142.

Warton DI, Wright IJ, Falster DS, Westob M. 2006. Bivariateline-fitting methods for allometry. Biol Rev 81:259–291.

Weinstein KJ. 2005. Body proportions in ancient Andeans fromhigh and low altitudes. Am J Phys Anthropol 128:569–585.

Wells LH. 1963. Stature in earlier races of mankind. In: Broth-well D, Higgs E, editors. Science in archaeology. New York:Basic Books. p365–378.



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